Elasticity of substitution

Elasticity of substitution is the elasticity of the ratio of two inputs to a production (or utility) function with respect to the ratio of their marginal products (or utilities). In a competitive market, it measures the percentage change in the ratio of two inputs used in response to a percentage change in their prices. It measures the curvature of an isoquant and thus, the substitutability between inputs (or goods), i.e. how easy it is to substitute one input (or good) for the other.

John Hicks introduced this concept in 1932. Joan Robinson independently discovered it in 1933 using a mathematical formulation that was equivalent to Hicks's, though that was not realized at the time.

Let the utility over consumption be given by ${\displaystyle U(c_{1},c_{2})}$. Then the elasticity of substitution is:

where ${\displaystyle MRS}$ is the marginal rate of substitution. The last equality presents ${\displaystyle MRS_{12}=p_{1}/p_{2}}$ which is a relationship from the first order condition for a consumer utility maximization problem in Arrow-Debreu interior equilibrium. Intuitively we are looking at how a consumer's relative choices over consumption items change as their relative prices change.

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